logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

Rewrite log₁₀ x = -3 in exponential form.

Back

x = 10^(-3) = 0.001.

Front

Evaluate log_x 16 = 1/2.

Back

x = 256.

Front

Evaluate log₄ 16.

Back

2.

Front

Write in logarithmic form: 5² = 25.

Back

log₅ 25 = 2.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the product rule for logarithms?

Back

log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule for logarithms?

Back

log_b(m^p) = p * log_b(m).